2023/09/19 by Allan Freitas, Freitas, Allan, Márcio S. Santos +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Annulus (botany) #Boundary (topology) #Boundary value problem #Combinatorics #Computer science #Constant (computer programming) #Curvature #Differential Geometry (math.DG) #Elasticity and Material Modeling #Ellipsoid #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Graph #Materials science #Mathematical analysis #Mathematics #Mean curvature #Physics #Rotation (mathematics) #Uniqueness
paper · pdf · doi:10.48550/arxiv.2309.10405
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/09/19 · openalex created_date 2023/09/22 · openalex updated_date 2026/07/28
In this paper, we work with the existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. Under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor, we classify the CMC free boundary hypersurfaces as topological disks or annulus. Also, we construct some examples of free boundary minimal surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.